
Journal of Lie Theory 21 (2011), No. 2, 457468 Copyright Heldermann Verlag 2011 Automorphism Groups of Some Stable Lie Algebras Jongwoo Lee Graduate School of Railroad, National University of Technology, 172 Kongneungdong Nowongu, Seoul, Korea saganlee@snut.ac.kr Xueqing Chen Dept. of Mathematics and Computer Sciences, Univ. of Wisconsin, Whitewater, WI 53190, U.S.A. chenx@uww.edu Seul Hee Choi Dept. of Mathematics, University of Jeonju, Jeonju 560759, Korea chois@jj.ac.kr KiBong Nam Dept. of Mathematics and Computer Sciences, Univ. of Wisconsin, Whitewater, WI 53190, U.S.A. namk@uww.edu A degree stable Lie algebra is defined in the paper of KBong Nam, and Seul Hee Choi [Degree Stable Lie Algebras I, Algebra Colloquium 13 (2006) 487494]. The automorphism group Aut_{Lie}(S^{+}(2)) of the Lie algebra S^{+}(2) and the automorphism group of the Lie algebra W(1,0,2) are also found in this paper. We find the algebra automorphism groups of the Lie algebras W(1^{2},1,1) and W(1^{2},2,0) in this work. We show that the Cartan subalgebras of W(1^{2},1,1) and W(1^{2},2,0) are one dimensional. Keywords: Simple, Witt algebra, degreeing Lie algebra, Cartan subalgebra. MSC: 17A36 [ Fulltextpdf (313 KB)] for subscribers only. 